Question

The solution of the differential equation d y/y + dx/x = 0 is

Answer 1

The answer is given below :

RULE :

∫dx/x = logx + c, c = integral constant

SOLUTION :

Given,

dy/y + dx/x = 0

On integration, we get

∫dy/y + ∫dx/x = logc, logc = integral constant

⇒ logy + logx = logc

⇒ log(yx) = logc, since log(ab) = loga + logb

⇒ yx = c

⇒ xy = c,

which is the required solution.

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